为什么均值用总体5.4%，标准差用样本36

NO.PZ2015120604000178

问题如下：

BIM is a well-developed public company and its market capitalization growth rates over past few decades are normally distributed.The population has a mean of 10% and a standard deviation of 5.4%. An investor wants to figure out the probability that BIM's average capitalization growth rate will over 12.32% in the next three years (all the data are monthly statistics).Which of the following option is most accurate?

选项：

0.5%.

1%.

5%.

解释：

A is correct.

It is appropriate to use the central limit theroy to calculate. Standard error=5.4%/ $\sqrt {\rm{36}}$ P(X＞12.32%)=P(Z＞ (12.32%-10%)/0.009)=P(Z＞2.58). So the corresponding probability is 0.5%.

题目用标准正态分布公式，其中平均值和标准差统一用总体的值吗

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星星_品职助教 · 2022年02月02日

同学你好，

平均值用总体值是因为根据中心极限定理：样本均值（本题中的“average capitalization growth rate”）的均值就是总体均值μ。

分母用标准误同样是因为根据中心极限定理：样本均值的标准差（即标准误）为总体标准差σ除以根号n。在本题中n即为12×3=36.

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为什么均值用总体5.4%，标准差用样本36

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